Two similar circular loops carry equal currents in the same direction. On moving the coils further apart,the electric current will

In an $L-R$ circuit connected to a battery,the rate at which energy is stored in the inductor is plotted against time during the growth of the current in the circuit. Which of the following best represents the resulting curve?

$A$ coil is placed in a magnetic field of $1 \, T$. Its area changes at a rate of $\frac{5 \, m^2}{ms}$. If the current in the coil changes from $1 \, A$ to $2 \, A$ in $2 \times 10^{-3} \, s$,what is the inductance of the coil in $H$?

$A$ source of constant voltage $V$ is connected to a resistance $R$ and two ideal inductors $L_1$ and $L_2$ through a switch $S$ as shown. There is no mutual inductance between the two inductors. The switch $S$ is initially open. At $t=0$,the switch is closed and current begins to flow. Which of the following options is/are correct?
$[A]$ After a long time,the current through $L_1$ will be $\frac{V}{R} \frac{L_2}{L_1+L_2}$
$[B]$ After a long time,the current through $L_2$ will be $\frac{V}{R} \frac{L_1}{L_1+L_2}$
$[C]$ The ratio of the currents through $L_1$ and $L_2$ is fixed at all times $(t>0)$
$[D]$ At $t=0$,the current through the resistance $R$ is $\frac{V}{R}$

Two circular coils $P$ and $Q$ are fixed coaxially and carry currents $I_1$ and $I_2$ respectively.

$A$ wire loop is placed in a region of time-varying magnetic field which is oriented orthogonally to the plane of the loop as shown in the figure. The graph shows the magnetic field variation as a function of time. Assume the positive $emf$ is the one which drives a current in the clockwise direction as seen by the observer in the direction of $B$. Which of the following graphs best represents the induced $emf$ as a function of time?